Correlation - Statistics

Exploring Correlations: Understanding Statistical Methods When it comes to analyzing data, one of the most crucial aspects is understanding the relationship between different variables. Statistical methods allow us to measure and interpret these correlations, providing insights that can help us make informed decisions. In this article, we will explore the concept of correlations, and the statistical method that is commonly used to measure them: Pearson correlation. What is Pearson Correlation? Pearson correlation is a statistical method that measures the strength of the linear relationship between two continuous numerical variables. It is also referred to as the Pearson product-moment correlation coefficient, named after its creator, Karl Pearson. The Pearson correlation coefficient is a measure of the degree of correlation between two variables, with values ranging from -1 to 1. Interpreting Pearson Correlation Coefficient and P-Value The Pearson correlation method provides two values: the correlation coefficient and the P-value. The correlation coefficient represents the strength and direction of the relationship between the variables. A value close to 1 implies a large positive correlation, while a value close to negative 1 implies a large negative correlation, and a value close to zero implies no correlation between the variables. On the other hand, the P-value tells us how certain we are about the correlation that we calculated. A value less than.001 gives us a strong certainty about the correlation coefficient that we calculated. A value between.001 and.05 gives us moderate certainty. A value between.05 and.1 will give us a weak certainty. And a P-value larger than.1 will give us no certainty of correlation at all. When determining the strength of a correlation, we can say that there is a strong correlation when the correlation coefficient is close to 1 or negative 1, and the P-value is less than.001. A moderate correlation is when the correlation coefficient is between.5 and.8, and the P-value is between.001 and.05. A weak correlation is when the correlation coefficient is between.3 and.5, and the P-value is between.05 and.1. Finally, no correlation is when the correlation coefficient is close to zero, or when the P-value is larger than.1. To illustrate this, let's look at an example of the correlation between the variable horsepower and car price. Using the SI/PI stats package, we can easily calculate the Pearson correlation. In this example, the correlation coefficient is approximately.8, which is close to 1, indicating a strong positive correlation between horsepower and car price. The P-value is also very small, much less than.001, giving us strong certainty about the correlation. Creating a Correlation Heatmap Once we have calculated the Pearson correlation coefficient for each variable, we can create a correlation heatmap to visualize the relationships between the variables. A correlation heatmap is a graphical representation of the correlation matrix, where each cell represents the correlation coefficient between two variables. The heatmap uses a color scheme to indicate the strength of the correlation between two variables. A dark red color indicates a high positive correlation, while a dark blue color indicates a high negative correlation. A white color indicates no correlation. When we create a correlation heatmap for all the variables, we can see a diagonal line with a dark red color, indicating that all the values on this diagonal are highly correlated. This makes sense because when you look closer, the values on the diagonal are the correlation of all variables with themselves, which will be always 1. The correlation heatmap gives us a good overview of how the different variables are related to one another, and most importantly, how these variables are related to price. We can see that the variables horsepower and car weight have a high positive correlation with car price, while the variable engine displacement has a moderate positive correlation.